We develop a framework for continuous search for information on a choice set of multiple alternatives, and apply it to consumer search in a product market. When a consumer considers purchasing a product in a product category, the consumer can gather information sequentially on several products. At each moment the consumer can choose which product to gather more information on, and whether to stop gathering information and purchase one of the products, or decide not to purchase any of the available products. Given costly information gathering, consumers end up not gathering complete information on all the products, and need to make decisions under imperfect information. We solve for the optimal search, switch, and purchase or exit behavior in such a setting, which is characterized by an optimal consideration set and purchase thresholds. The paper shows that products are only searched if they have a sufficiently high expected valuation, and that, given that there are multiple products in the consumer’s consideration set, the consumer only stops searching for information and purchases a product if the expected valuation of the product is sufficiently greater than the expected valuations of alternative products. Comparative statics show that negative information correlation among products widens the purchase threshold, and so does an increase in the size of the choice set. We also show that a higher expected valuation of one product might lead to lower sales of all products combined, and that it may be optimal for sellers of multiple products to obfuscate information for high-valuation products, while facilitate consumer search for low-valuation ones.